Is there any way to automate the export of one or more .pst files, by searching for content?

If you mean you want to automate the process of exporting content search/eDiscovery, follow the steps here: Export to PST via Powershell | Microsoft Community Hub

Alternatively, you can use the Graph API, but it's currently only available for eDiscovery Premium: https://www.michev.info/blog/post/5806/using-the-graph-api-to-export-ediscovery-premium-datasets